Quantum physics vol.2 From Time-Dependent Dynamics to Many-Body Physics and Quantum Chaos

Zelevinsky, V.Quantum physics   vol.2 From Time-Dependent Dynamics to Many-Body Physics and Quantum Chaos(Wiley-VCH,2011)(ISBN 9783527410576)(600dpi)(581p) ......Page 4
Copyright iv ......Page 5
Contents v ......Page 6
Preface xiii  ......Page 13
1.1 Transition Probability 1 ......Page 15
1.2 Perturbative Solution 2 ......Page 16
1.3 Formal Series 5 ......Page 19
1.4 Adiabatic Perturbations 7 ......Page 21
1.5 Adiabatic Perturbation Theory 8 ......Page 22
1.6 Nonadiabatic Transitions 10 ......Page 24
1.7 Geometric Phase 13 ......Page 27
1.8 Sudden Perturbations 16 ......Page 30
1.9 Shake-Off Processes 19 ......Page 33
2.1 Golden Rule 23 ......Page 37
2.3 Degenerate States 26 ......Page 40
2.4 Quasienergy 28 ......Page 42
2.5 Final States in the Continuum 29 ......Page 43
2.6 Rotating Wave Approximation 35 ......Page 49
2.7 Interaction with the Quantized Field 38 ......Page 52
2.8 Dressed States 41 ......Page 55
2.9 Super-Radiance 42 ......Page 56
3.1 Scattering and Cross Section 47 ......Page 61
3.2 Rutherford Scattering 49 ......Page 63
3.3 Static Form-Factor 51 ......Page 65
3.4 Screening 54 ......Page 69
3.5 Atomic Excitation and Ionization 56 ......Page 70
3.6 Energy Losses 58 ......Page 72
3.7 Coulomb Excitation 60 ......Page 74
4.1 \tIntroduction: Classical and Quantum Field 63 ......Page 77
4.2 Hamiltonian Description of the Radiation Field 64 ......Page 78
4.3 Quantization of the Radiation Field 67 ......Page 81
4.4 Photon Wave Function 71 ......Page 85
4.5 Vector Spherical Harmonics 73 ......Page 87
4.6 Casimir Effect 75 ......Page 89
4.7 Euler-Maclaurin Summation Formula 77 ......Page 91
4.8 Lamb Shift 79 ......Page 93
4.9 Interaction of Radiation with Matter 82 ......Page 96
5.1 Einstein Coefficients; Masers and Lasers 87 ......Page 101
5.2 Photoabsorption 91 ......Page 105
5.3 Long Wavelength Limit 92 ......Page 106
5.4 Higher Multipole Transitions 95 ......Page 109
5.5 Stimulated and Spontaneous Radiation 97 ......Page 111
5.6 Dipole Radiation 98 ......Page 112
5.7 Selection Rules and Examples 100 ......Page 114
5.8 Photoelectric Effect 103 ......Page 117
6.1 Macroscopic Description 107 ......Page 121
6.2 Linear Response 108 ......Page 122
6.3 Causality 110 ......Page 124
6.4 Dielectric Function 112 ......Page 126
6.5 Dispersion Properties 114 ......Page 128
6.6 Quantum Damping 116 ......Page 130
6.7 Dispersion Relations 118 ......Page 132
6.8 Description of Scattering 119 ......Page 133
6.9 Scattering Cross Section 121 ......Page 135
6.10 Coherent Scattering 123 ......Page 137
6.11 Resonance Fluorescence 124 ......Page 138
6.12 S cattering off Many Centers 125 ......Page 139
7.1 Scattering and Observables 129 ......Page 143
7.2 Classical Scattering and Cross Section 130 ......Page 144
7.3 Scattering Matrix 133 ......Page 147
7.4 Transition Rate 134 ......Page 148
7.5 B orn Approximation 136 ......Page 150
7.6 Continuity Equation 138 ......Page 152
7.7 Elastic Scattering 139 ......Page 153
7.8 Unitarity and Optical Theorem 140 ......Page 154
7.9 Green Function 142 ......Page 156
7.10 Born Series 145 ......Page 159
7.11 Validity of the Born Approximation 148 ......Page 162
7.12 Scattering at High Energies 150 ......Page 164
8.1 Partial Wave Analysis 153 ......Page 167
8.2 Elastic and Inelastic Cross Sections 155 ......Page 169
8.3 Elastic Phase Shifts 156 ......Page 170
8.4 Analyticity 157 ......Page 171
8.5 Scattering at Low Energies: Examples 158 ......Page 172
8.6 Phases and Their Energy Behavior 162 ......Page 176
8.7 Scattering Length 165 ......Page 179
8.8 Resonance Scattering at Low Energies 168 ......Page 182
8.9 Effective Radius 171 ......Page 185
8.10 Scattering with Spin-Orbit Interaction 172 ......Page 186
8.11 Polarization and Azimuthal Asymmetry 175 ......Page 189
9.1 Classical and Non-classical Scattering 179 ......Page 193
9.2 Semiclassical Amplitude 180 ......Page 194
9.3 Semiclassical Phases 181 ......Page 195
9.4 Relation to the Eikonal Approximation 185 ......Page 199
9.5 Diffraction Scattering 186 ......Page 200
9.6 Diffraction from a Black Sphere 188 ......Page 202
9.7 Optical Model 190 ......Page 204
9.8 Multiple Scattering in the Medium 192 ......Page 206
9.9 Coherent Scattering in Crystals 196 ......Page 210
10.1 Reaction Channels 199 ......Page 213
10.2 Scattering Matrix for Many-Channel Reactions 200 ......Page 214
10.3 Detailed Balance 202 ......Page 216
10.4 Cross Sections for Slow Particles 204 ......Page 218
10.5 Thresholds and Unitarity 206 ......Page 220
10.6 Isolated Resonance; Exponential and Non-exponential Decay 209 ......Page 223
10.7 Quantum Zeno Effect 210 ......Page 224
10.8 Resonance Cross Section 215 ......Page 229
10.9 Unitarity and Super- Radiance 217 ......Page 231
10.10 Angular Momentum and Parity 218 ......Page 232
10.11 Narrow Resonance as a Compound System 219 ......Page 233
10.12 Interference of Resonance and Potential Scattering 221 ......Page 235
11.1 Limitations of the Approach 225 ......Page 239
11.3 Lor entz Transformation 226 ......Page 240
11.4 Energy and Momentum 227 ......Page 241
11.5 Tensors and Notations 229 ......Page 243
11.6 Klein-Gordon Equation 231 ......Page 245
11.7 Current Conservation 233 ......Page 247
11.8 Particles and Antiparticles 234 ......Page 248
11.9 Electromagnetic Field 236 ......Page 250
11.10 Minimal Electromagnetic Coupling 237 ......Page 251
11.11 Photoabsorption at Higher Energies 240 ......Page 254
11.12 Nuclear Photoeffect 242 ......Page 256
11.13 Estimates of Processes in QED 244 ......Page 258
12.1 Introducing the Dirac Equation 249 ......Page 263
12.2 Covariant Form and Algebra 251 ......Page 265
12.3 Current 253 ......Page 267
12.4 Charge Conjugation 254 ......Page 268
12.5 Relativistic Transformations 256 ......Page 270
12.6 Spin Operator 258 ......Page 272
12.7 Bilinear Covariants 260 ......Page 274
13.1 Free Motion 265 ......Page 279
13.2 Dirac Sea 266 ......Page 280
13.3 Explicit Solutions 267 ......Page 281
13.4 Complete Set of Solutions 270 ......Page 284
13.5 Pauli Equation 273 ......Page 287
13.6 Second Order Effects 274 ......Page 288
13.7 Central Field 276 ......Page 290
13.8 Coulomb Field 279 ......Page 293
13.9 Static Uniform Magnetic Field 283 ......Page 297
14.1 Parity Transformation for a Dirac Particle 285 ......Page 299
14.2 Time-Reversal Transformation 287 ......Page 301
14.3 CVT Transformation 288 ......Page 302
14.4 Massless Particles 289 ......Page 303
14.5 Neutrinos in the Massless Limit 291 ......Page 305
14.6 Parity Non-conservation Revisited 293 ......Page 307
14.7 Neutrino Oscillations 295 ......Page 309
14.8 Majorana Neutrinos 297 ......Page 311
14.9 Strangeness 299 ......Page 313
14.10 Neutral Kaons and CP-parity 300 ......Page 314
14.11 Neutral Kaons and Quantum Regeneration 303 ......Page 317
15.1 Indistinguishable Particles 307 ......Page 321
15.2 Permutational Symmetry 308 ......Page 322
15.3 Bosons and Fermions 310 ......Page 324
15.4 Wave Functions of Noninteracting Particles 312 ......Page 326
15.5 Two-Nucleon States 315 ......Page 329
15.6 Scattering of Identical Particles 324 ......Page 338
15.7 Intensity Interferometry 328 ......Page 342
16.1 Introducing Isospin 331 ......Page 345
16.2 Isospin Invariance 333 ......Page 347
16.3 Isospin of Many-Body Systems 334 ......Page 348
16.4 Isospin and Space-Spin Symmetry 336 ......Page 350
16.5 A Glimpse of a More General Picture 338 ......Page 352
16.6 Relations between Cross Sections 340 ......Page 354
17.1 Occupation Number Representation 345 ......Page 359
17.2 Introduction to Secondary Quantization 347 ......Page 361
17.3 Bose-Statistics 348 ......Page 362
17.4 Fermi-Statistics 350 ......Page 364
17.5 Algebraic Relations 351 ......Page 365
17.6 One-Body Operators 352 ......Page 366
17.7 Two-Body Operators 356 ......Page 370
17.8 Interparticle Interaction in the Plane-Wave Basis 357 ......Page 371
17.9 Interparticle Interaction in a Finite System 359 ......Page 373
18.1 Independent Particle Approximation 363 ......Page 377
18.2 Adding Rotational Invariance 364 ......Page 378
18.3 Many-Particle Configurations 366 ......Page 380
18.4 Exchange Interaction 370 ......Page 384
18.5 Two-Electron System 372 ......Page 386
18.6 Helium Atom: Optical Spectrum 375 ......Page 389
18.7 Hund’s Rules 376 ......Page 390
18.8 Particle-Hole Symmetry 378 ......Page 392
18.9 Shell Structure 380 ......Page 394
19.1 Ideal Fermi-Gas 383 ......Page 397
19.2 Spin Paramagnetism 388 ......Page 402
19.3 Orbital Diamagnetism 391 ......Page 405
19.4 Introducing Mean Field 393 ......Page 407
19.5 Statistical Model 395 ......Page 409
19.6 Screening in the Electron Gas 398 ......Page 412
19.7 Hartree-Fock Approximation 399 ......Page 413
19.8 Spatially Uniform System 402 ......Page 416
19.9 Coulomb Gas 404 ......Page 418
19.10 Density Functional Theory 406 ......Page 420
20.1 Linear Chain 409 ......Page 423
20.2 Phonons 413 ......Page 427
20.3 Phonon Modes 415 ......Page 429
20.4 Spin Waves 418 ......Page 432
20.5 Particle-Hole Excitations 424 ......Page 438
20.6 Density Fluctuations 426 ......Page 440
20.7 Random Phase Approximation 428 ......Page 442
20.8 Electron-Phonon Interaction 429 ......Page 443
21.1 Bose-Einstein Condensation 433 ......Page 447
21.2 Condensate as a Reservoir; Chemical Potential 435 ......Page 449
21.3 Weakly Non-ideal Gas 437 ......Page 451
21.4 Phonons 439 ......Page 453
21.5 Superfluidity 441 ......Page 455
21.6 Canonical Transformation 442 ......Page 456
21.7 Phonons as Density Waves 445 ......Page 459
21.8 Local Density Approximation 447 ......Page 461
21.9 Non-uniform Gas 450 ......Page 464
22.1 Pairing 453 ......Page 467
22.2 Pairs and Seniority 455 ......Page 469
22.3 Multipole Moments in the Seniority Scheme 458 ......Page 472
22.4 Degenerate Model and Quasispin 459 ......Page 473
22.5 Canonical Transformation 462 ......Page 476
22.6 BCS Theory and Trial Wave Function 466 ......Page 480
22.7 Energy Minimization 467 ......Page 481
22.8 Energy Gap 469 ......Page 483
22.9 Excitation Spectrum 473 ......Page 487
22.10 Condensation Energy 477 ......Page 491
22.11 Transition Amplitudes 478 ......Page 492
23.1 Mixed States and Density Matrix 481 ......Page 495
23.2 Properties of the Density Matrix 482 ......Page 496
23.3 Thermal Equilibrium 486 ......Page 500
23.4 Polarization Density Matrix 489 ......Page 503
23.5 Application of Scattering 493 ......Page 507
23.6 Ensemble Entropy 496 ......Page 510
23.7 Evolution of the Density Matrix 498 ......Page 512
23.8 Linear Response Revisited 500 ......Page 514
23.9 Electric Conductivity 501 ......Page 515
24.1 Classical and Quantum Chaos 505 ......Page 519
24.2 Local Spectral Statistics: Poisson Distribution 508 ......Page 522
24.3 Gaussian Orthogonal Ensemble 512 ......Page 526
24.4 Level Spacing Distribution 514 ......Page 528
24.5 GOE and Information 517 ......Page 531
24.6 Universality Classes 518 ......Page 532
24.7 Semicircle Law 521 ......Page 535
24.8 Chaotic Eigenfunctions 527 ......Page 541
24.9 Complexity and Information Entropy 531 ......Page 545
24.10 Porter-Thomas and Related Distributions 533 ......Page 547
25.1 Entanglement 535 ......Page 549
25.2 Teleportation 536 ......Page 550
25.3 Mathematics of Entanglement 538 ......Page 552
25.4 Quantum Bell Inequalities 541 ......Page 555
25.5 EPR(B) Paradox and Hidden Variables 543 ......Page 557
25.6 Experimental Tests 546 ......Page 560
25.7 Decoherence and Measurement Paradox 547 ......Page 561
References 551 ......Page 565
Further Reading 555 ......Page 569
Index 563 ......Page 577
cover ......Page 1